Quanser Engineering Trainer for NI-ELVIS. QNET Rotary Pendulum Trainer. Student Manual. QNET-011 ROTPEN Trainer

Transcription

1 QNET-011 ROTPEN Trainer Quanser Engineering Trainer for NI-ELVIS QNET Rotary Pendulum Trainer Student Manual Under the copyright laws, this publication may not be reproduced or transmitted in any form, electronic or mechanical, including photocopying, recording, storing in an information retrieval system, or translating, in whole or in part, without the prior written consent of Quanser Inc. Copyright 2009, by Quanser Inc. All rights reserved.

2 Table of Contents 1. INTRODUCTION PREREQUISITES ROTPENT VIRTUAL INSTRUMENTS Summary Description Simple Modeling Control Design Swing-Up Control IN-LAB EXPERIMENTS Simple Modeling Dampening Friction Moment of Inertia Exercises Balance Control Design Model Analysis Control Design and Simulation Exercises Swing-Up Control Default Balance Control Implement Designed Balance Controller Balance Control with Friction Compensation Energy Control Hybrid Swing-Up Control Exercises...27 Document Number 859 Revision 1.0 Page i

3 5. REFERENCES...33 Document Number 859 Revision 1.0 Page ii

4 1. Introduction This manual contains experimental procedures and lab exercises for the QNET Rotary Pendulum Trainer (ROTPENT). The ROTPENT is depicted in Figure 1 and the hardware of the device is explained in Reference [1]. Figure 1: QNET rotary pendulum trainer on ELVIS II. The prerequisites to run the LabVIEW Virtual Instruments (VIs) for the ROTPENT are listed in Section 2 and described in Section 3. The in-lab procedures are given in Section 4 and split into three sections: simple modeling, balance control design, and swing-up control. In Section 4.1, the coupling and friction of the system are assessed and the moment of inertia is found. The controller that balances the inverted pendulum is designed in Section 4.2 and then implemented in Section 4.3. In addition to running the balance controller, the energy-based swing-up control is implemented in Section 4.3. The exercises are given within the lab procedures and labeled Exercise. In that case, enter your answer in the exercises number in the corresponding section. 2. Prerequisites The following system is required to run the QNET ROTPENT virtual instruments: PC equipped with either: Document Number 859 Revision 1.0 Page 1

5 NI-ELVIS I and an NI E-Series or M-Series DAQ card. NI ELVIS II Quanser Engineering Trainer (QNET) module. LabVIEW with the following add-ons: DAQmx Control Design and Simulation Module When using ELVIS II: ELVISmx installed for required drivers. When using ELVIS I: ELVIS CD or later installed. If these are not all installed then the VI will not be able to run! Please make sure all the software and hardware components are installed. If an issue arises, then see the troubleshooting section in Reference [1]. 3. ROTPENT Virtual Instruments 3.1. Summary Table 1 below lists and describes the ROTPENT LabVIEW VIs supplied with the QNET CD. VI Description QNET_ROTPENT_Simple_Modeling.vi Apply voltage to DC motor and examine the arm and pendulum responses. QNET_ROTPENT_Control_Design.vi Design and simulate LQR-based balance controller. QNET_ROTPENT_Swing_Up_Control.vi Swing-up and balance pendulum. Table 1: ROTPENT VIs supplied with the QNET CD Description Simple Modeling The QNET-ROTPENT Simple Modeling VI is shown in Figure 2. It runs the DC motor connected to the pendulum arm in open-loop and plots the corresponding pendulum arm and link angles as well as the applied input motor voltage. Table 2 lists and describes the main elements of the ROTPENT Simple Modeling virtual instrument front panel. Every element is uniquely identified through an ID number and located in Figure 2. Document Number 859 Revision 1.0 Page 2

6 Figure 2: QNET-ROTPENT Simple Modeling VI. ID # Label Parameter Description Unit 1 Theta θ Arm angle numeric display measured by encoder on motor. deg 2 Alpha α Pendulum angle numeric display measured deg by encoder on pendulum pivot. 3 Current Im Motor armature current numeric display. A 4 Voltage Vm Motor input voltage numeric display. V 5 Signal Type Type of signal generated for the input voltage signal. 6 Amplitude Generated signal amplitude input box. V 7 Frequency Generated signal frequency input box. Hz 8 Offset Generated signal offset input box. V Document Number 859 Revision 1.0 Page 3

7 9 Disturbance Vsd 10 Device Selects the NI DAQ device. 11 Sampling Rate Sets the sampling rate of the VI. 12 Stop Stops the LabVIEW VI from running. 13 Scopes: Angle 14 Scopes: Voltage Vm θ,α Apply simulated disturbance voltage. V Hz Scope with measured arm angle (in red) deg and pendulum angle (in blue). Scope with applied motor voltage (in red). V Table 2: Nomenclature of QNET-ROTPENT Simple Modeling VI Control Design The QNET ROTPENT Control Design VI enables users to design a balance controller and simulate its response. The matrices for the state-space model of the rotary inverted pendulum system is shown in the Symbolic Model tab and illustrated in Figure 4. The values of the variables used in the state-space model can be changed. In the Open Loop Analysis tab, shown in Figure 5, the numerical state-space model is displayed and the resulting open-loop poles are plotted on a phase plane. Based on this model, a controller to balance the rotary inverted pendulum system can be designed using the Linear-Quadratic Regulator (LQR) optimization technique, as shown in the Simulation tab in Figure 6. The resulting closed-loop inverted pendulum system can be simulated. Table 3 lists and describes the main elements of the ROTPENT Control Design virtual instrument user interface. Every element is uniquely identified through an ID number and located in figures 4, 5, and 6. Document Number 859 Revision 1.0 Page 4

8 Figure 3: QNET ROTPENT Control Design VI: Symbolic Model tab. Document Number 859 Revision 1.0 Page 5

9 Figure 4: QNET ROTPENT Control Design VI: "Open Loop Analysis" tab. Document Number 859 Revision 1.0 Page 6

10 Figure 5: QNET ROTPENT Control Design VI: "Simulation" tab. ID # Label Parameter Description Unit 1 Mp Mp Mass of pendulum assembly (link + weight). kg 2 lp lp Center of mass of pendulum assembly (link+weight) input box. m 3 r r Length from motor shaft to pendulum pivot. m 4 Jp Jp Pendulum moment of inertia relative to pivot. kg.m2 5 Jeq Jeq Equivalent moment of inertia acting on the DC motor shaft. kg.m2 6 Bp Bp Viscous damping about the pendulum pivot. N.m.s/ra d 7 Beq Beq Equivalent viscous damping acting on the N.m.s/ra Document Number 859 Revision 1.0 Page 7

11 DC motor shaft. d 8 Kt Kt DC motor current-torque constant. N.m/A 9 Km Km DC motor back-emf constant. V.s/rad 10 Rm Rm Electrical resistance of the DC motor armature. ohm 11 Symbolic A A Rotary pendulum linear state-space matrix A. 12 Symbolic B B Rotary pendulum linear state-space matrix B. 13 Symbolic C C Rotary pendulum linear state-space matrix C. 14 Symbolic D D Rotary pendulum linear state-space matrix D. 15 Stop Stops the LabVIEW VI from running. 16 Error Out Displays any error encountered in the VI. 17 Open-Loop Equation Numeric linear state-space model of rotary pendulum. 18 Pole-Zero Map Maps pole and zeros of open-loop rotary pendulum system. 19 Signal Type Type of signal generated for the arm position reference. 20 Amplitude Generated signal amplitude input box. V 21 Frequency Generated signal frequency input box. Hz 22 Offset Generated signal offset input box. V 23 Disturbance Vsd Apply simulated disturbance voltage. V 24 Q Q Linear-quadratic weighting matrix that defines a penalty on the state. 25 R R Linear-quadratic weighting matrix that defines a penalty on the control action. 26 Optimal Gain (K) K State-feedback control gain calculated uisng LQR. 27 Arm θ Scope with reference (in blue) and measured deg (in red) arm angles. 28 Pendulum α Scope with inverted pendulum angle (in deg blue). 29 Control Input Vm Scope with applied motor voltage (in red). V Table 3: Nomenclature of QNET-ROTPENT Control Design VI. Document Number 859 Revision 1.0 Page 8

12 Swing-Up Control The QNET rotary pendulum trainer swing-up control VI implements an energy-based control that swings up the pendulum to its upright vertical position and a state-feedback controller to balance the pendulum when in its upright position. The main elements of the VI front panel are summarized in Table 4 and identified in Figure 6 through the corresponding ID number. Figure 6: QNET ROTPENT Swing-Up Control. Document Number 859 Revision 1.0 Page 9

13 # Label Parameter Description Unit 1 Theta θ Arm angle measured by encoder on motor. deg 2 Alpha α Pendulum angle measured by encoder on pendulum pivot. deg 3 Current Im Motor armature current numeric display. A 4 In Range? Balance controller is engaged when this LED is turns bright green. 5 Energy Numeric display of the pendulum energy. 6 Signal Type Type of signal generated for the input voltage. 7 Amplitude Generated signal amplitude input box. V 8 Frequency Generated signal frequency input box. Hz 9 Offset Generated signal offset input box. V mj 10 Disturbance Vsd Apply simulated disturbance voltage. V 11 Amplitude Ad Dither signal amplitude input box. V 12 Frequency fd Dither signal frequency input box. Hz 13 Offset Vd0 Dither signal offset input box. V 14 kp_theta kp,θ Arm angle proportional gain input box. V/rad 15 kp_alpha kp,α Pendulum angle proportional gain input box. V/rad 16 kd_theta kd,θ Arm angle derivative gain input box. V.s/rad 17 kd_alpha kd,α Pendulum angle derivative gain input box. V.s/rad 18 mu µ Proportional gain for energy controller. m/(s2.j) 19 Er Er Reference energy for energy controller. mj 20 Max accel umax Maximum acceleration m/s2 21 Activate Swing Up When pressed down the energy controller that swingsup the pendulum is engaged. 22 Mp Mp Mass of pendulum assembly (link + weight). kg 23 lp lp Center of mass of pendulum assembly (link+weight) input box. m 24 Marm Marm Mass of rotary arm. kg 25 r r Length from motor shaft to pendulum pivot. m Document Number 859 Revision 1.0 Page 10

14 26 Jp Jp Pendulum moment of inertia relative to pivot. kg.m2 27 Jeq Jeq Equivalent moment of inertia acting on the DC motor shaft. kg.m2 28 Kt Kt Current-torque or back-emf constant: they are equivalent in SI units. N.m/A 29 Rm Rm Electrical resistance of the DC motor armature. ohm 30 Device Selects the NI DAQ device. 31 Sampling Rate Sets the sampling rate of the VI. 32 Stop Stops the LabVIEW VI from running. 33 Angle / Energy θ, α, E Scope with measured arm angle (in red), measured pendulum angle (in blue), and pendulum energy (in green). deg/mj Scope with applied motor voltage (red). V 34 Voltage Vm Hz Table 4: Nomenclature of QNET ROTPENT Swing-Up Control VI. 4. In-Lab Experiments 4.1. Simple Modeling Dampening Open the QNET_ROTPENT_Simple_Modeling.vi. Ensure the correct Device is chosen, as shown in Figure 7 Figure 7: Selecting correct device Run the QNET_ROTPENT_Simple_Modeling.vi, shown in Figure 8. Hold the arm of the rotary pendulum system stationary and manually perturb the pendulum. While still holding the arm, examine the response of Pendulum Angle (deg) in the Angle (deg) scope. This is the response from the pendulum system. Repeat Step 3 above and release the arm after several swings. Document Number 859 Revision 1.0 Page 11

15 7. 8. Exercise 1: Examine the Pendulum Angle (deg) response when the arm is not fixed. This is the response from the rotary pendulum system. Given the response from these two systems pendulum and rotary pendulum which converges faster towards angle zero? Why does one system dampen faster than the other? Stop the VI by clicking on the Stop button. Figure 8: QNET ROTPEN Simple Modeling VI Friction 1. Run the QNET_ROTPENT_Simple_Modeling.vi. 2. In the Signal Generator section set: Amplitude = 0.00 V Frequency = 0.25 Hz Offset = 0.00 V 3. Change the Offset in steps of 0.10 V until the pendulum begins moving. Record the voltage at which the pendulum moved. 4. Repeat Step 3 above for steps of V. Document Number 859 Revision 1.0 Page 12

16 5. Exercise 2: Enter the positive and negative voltage values needed to get the pendulum moving in. Why does the motor need a certain amount of voltage to get the motor shaft moving? 6. Stop the VI by clicking on the Stop button Moment of Inertia 1. Exercise 3: Using references [1] and [2], calculate the moment of inertia acting about the pendulum pivot. 2. Run the QNET_ROTPENT_Simple_Modeling.vi 3. In the Signal Generator section set: Amplitude = 1.00 V Frequency = 0.25 Hz Offset = 0.00 V 4. Click on the Disturbance toggle switch to perturb the pendulum and measure the amount of time it takes for the pendulum to swing back-and-forth in a few cycles (e.g. 4 cycles). 5. Exercise 4: Find the frequency and moment of inertia of the pendulum using the observed results. See Reference [2] to see how to calculate the inertia experimentally and make sure you fill in Table Exercise 5: Compare the moment of inertia calculated analytically in Exercise 3 and the moment of inertia found experimentally. Is there a large discrepancy between them? 7. Stop the VI by clicking on the Stop button Exercises Exercise 1: Dampening Document Number 859 Revision 1.0 Page 13

17 Exercise 2: Friction Analysis Description Symbol Value Unit Positive Coulomb Friction Voltage Vfp V Negative Coulomb Friction Voltage Vfn V Exercise 3: Calculate Moment of Inertia Document Number 859 Revision 1.0 Page 14

18 Exercise 4: Measure Moment of Inertia Description Symbol Value Unit Cycles ncyc Duration t s Frequency f Hz Pendulum moment of inertia Jp,exp kg.m2 Table 5: Measure pendulum moment of inertia. Exercise 5: Comparing Pendulum Inertia 4.2. Balance Control Design Model Analysis Open the QNET_ROTPENT_Control_Design.vi, shown in Figure 9. Run the QNET_ROTPENT_Control_Design.vi. Select the Symbolic Model tab. The Model Parameters array includes all the rotary pendulum modeling variables that are used in the state-space matrices A, B, C, and D. Select the Open Loop Analysis tab. Exercise 1: This shows the numerical linear state-space model and a pole-zero plot of the open-loop inverted pendulum system. What do you notice about the location of the open-loop poles? Recommended: In the Model Parameters section, it is recommend to enter the pendulum moment of inertia, Jp, determined experimentally in Section In the Symbolic Model tab, set the pendulum moment of inertia, Jp, to 1.0e-5 kg.m2. Document Number 859 Revision 1.0 Page 15

19 8. Exercise 2: Select the Open Loop Analysis tab. How did the locations of the open-loop poles change with the new inertia? Enter the pole locations of each system with a different moment of inertia in Table 6. Are the changes of having a pendulum with a lower inertia as expected? 9. Reset the pendulum moment of inertia, Jp, back to 1.77e Stop the VI by clicking on the Stop button. Figure 9: QNET ROTPEN trainer control design VI: Symbolic Model tab Control Design and Simulation Open the QNET_ROTPENT_Control_Design.vi, shown in Figure 10. Select the Simulation tab. Run the QNET_ROTPENT_Control_Design.vi. In the Signal Generator section set: Amplitude = 45.0 deg Frequency = 0.20 Hz Offset = 0.0 deg Document Number 859 Revision 1.0 Page 16

20 Set the Q and R LQR weighting matrices to the following: Q(1,1) = 10, i.e. set first element of Q matrix to 5. R = 1.00 Changing the Q matrix generates a new control gain. Exercise 3: The arm reference (in red) and simulated arm response (in blue) are shown in the Arm (deg) scope. How did the arm response change? How did the pendulum response change in the Pendulum (deg) scope. Set the third element in the Q matrix to 0, i.e. Q(3,3) = 0. Exercise 4: Examine and describe the change in the Arm (deg) and Pendulum (deg) scope. By varying the diagonal elements of the Q matrix, design a balance controller that adheres to the following specifications: Arm peak time less than 0.75 seconds: tp 0.75 s Motor voltage peak less than ± 12.5 V: Vm 12.5 V Pendulum angle less than 10.0 degrees: α 10.0 deg Exercise 5: Enter the Q and R matrices along with and control gain used to meet the specifications. Exercise 6: Attach the responses from the Arm (deg), Pendulum (deg), and Control Input (V) scopes when using your designed balance controller. Stop the VI by clicking on the Stop button. Document Number 859 Revision 1.0 Page 17

21 Figure 10: QNET ROTPEN trainer control design VI: Simulation tab. Document Number 859 Revision 1.0 Page 18

22 Exercises Exercise 1: Open-Loop Poles Exercise 2: Effect of Changing Inertia on Poles Description Symbol System w/ Jp = 1.7e-4 p0 rad/s p1 rad/s p2 rad/s p3 rad/s p0 rad/s p1 rad/s p2 rad/s p3 rad/s System w/ Jp = 1.00e-5 Value Unit Table 6: Effect on poles when changing moment of inertia. Document Number 859 Revision 1.0 Page 19

23 Exercise 3: Arm Response with Q(1,1)=10 Exercise 4: Arm Response with Q(3,3)=0 Document Number 859 Revision 1.0 Page 20

24 Exercise 5: Designed Balance Controller Description Symbol Value Unit Q(1,1) Q1,1 Q(2,2) Q2,2 Q(3,3) Q3,3 Q(4,4) Q4,4 R R K(1) kp,θ V/rad K(2) kp,α V/rad K(3) kd,θ V.s/rad K(4) kd,α V.s/rad Table 7: Designed balance controller. Exercise 6: Balance Control Responses Document Number 859 Revision 1.0 Page 21

25 Document Number 859 Revision 1.0 Page 22

26 4.3. Swing-Up Control Default Balance Control Open the QNET_ROTPENT_Swing_Up_Control.vi, shown in Figure 11. Ensure the correct Device is chosen. Run the QNET_ROTPENT_Swing_Up_Control.vi. In the Signal Generator section set: Amplitude = 0.0 deg Frequency = 0.10 Hz Offset = 0.0 deg In the Balance Control Parameters section set: kp_theta = V/rad kp_alpha = 80 V/rad kd_theta = V/(rad/s) kd_alpha = 10.5 V/(rad/s) In the Swing-Up Control Parameters section set: mu = 55 m/s2/j Er = 20.0 mj max accel = 10 m/s2 Activate Swing-Up = OFF (de-pressed) Adjust the Angle/Energy (deg/mj) scope scales to see between -250 and 250 (see Reference [1] for help). Manually rotate the pendulum in the upright position until the In Range? LED in the Control Indicators section turns bright green. Ensure the encoder cable does not interfere with the pendulum arm motion. Exercise 1: Vary Offset and observe the Arm Angle (deg) response in the Angle/Energy (deg/mj) scope. Do not set the Offset too high or the encoder cable will interfere with the pendulum arm motion. Exercise 2: As the pendulum is being balanced, examine the red Arm Angle (deg) and blue Pendulum Angle (deg) responses in the Angle/Energy (deg/mj) scope. In the Signal Generator section set: Amplitude = 45.0 deg Frequency = 0.10 Hz Offset = 0.0 deg Exercise 3: Observe the behaviour of the system when a square wave command is given to the arm angle. Why does the arm initially move in the wrong direction? Click on the Stop button to stop running the VI. Document Number 859 Revision 1.0 Page 23

27 Figure 11: QNET rotary pendulum trainer swing-up VI Implement Designed Balance Controller Go through Section and design a balance control according to the given specifications. Remark: It is recommended to use the experimental determined pendulum moment of inertia that was found in Section Open the QNET_ROTPENT_Swing_Up_Control.vi. Ensure the correct Device is chosen. Run the QNET_ROTPENT_Swing_Up_Control.vi. In the Signal Generator section set: Amplitude = 45.0 deg Frequency = 0.20 Hz Offset = 0.0 deg To implement your balance controller, enter the control gain found in Section in kp_theta, kp_alpha, kd_theta, and kd_alpha in the Control Parameters section. Manually rotate the pendulum in the upright position until the In Range? LED in the Control Indicators section turns bright green. Ensure the encoder cable does not interfere with the Document Number 859 Revision 1.0 Page 24

28 8. 9. pendulum arm motion. Exercise 4: Attach the response found Angle/Energy (deg/mj) and the Voltage (V) scopes. Does your system meet the specifications given in Section 4.2.2? Click on the Stop button to stop running the VI Balance Control with Friction Compensation Go through steps 1-8 in Section to run the default balance control. In the Signal Generator section set: Amplitude = 0.0 deg Frequency = 0.10 Hz Offset = 0.0 deg 3. In the Dither Signal section set: Amplitude = 0.00 V Frequency = 2.50 Hz Offset = 0.00 V 4. Exercise 5: Observe the behaviour of Arm Angle (deg) in the Angle/Energy (deg/mj) scope. Intuitively speaking, can you find some reasons why the arm is oscillating? 5. Increase the Amplitude in the Dither Signal section by steps of 0.1 V until you notice a change in the arm angle response. 6. Exercise 6: From the Voltage (V) scope and the pendulum motion, what is the Dither signal doing? Compare the response of the arm with and without the Dither signal. 7. Increase the Frequency in the Dither Signal section starting from 1.00 to 10.0 Hz. 8. Exercise 7: How does this effect the pendulum arm response? 9. Optional Exercise 8: Set the Dither Signal properties according to the friction measured in Exercise 2 of the QNET-ROTPEN: Simple Modeling experiment. How does this effect the pendulum arm response? 10. Click on the Stop button to stop running the VI Energy Control Open the QNET_ROTPENT_Swing_Up_Control.vi. Ensure the correct Device is chosen. Run the QNET_ROTPENT_Swing_Up_Control.vi. In the Balance Control Parameters section ensure the following parameters are set: kp_theta = V/rad kp_alpha = 80.0 V/rad kd_theta = V/(rad/s) kd_alpha = 10.5 V/(rad/s) In the Swing-Up Control Parameters section set: mu = 55 m/s2/j Er = 20.0 mj max accel = 10 m/s2 Activate Swing-Up = OFF (de-pressed) Document Number 859 Revision 1.0 Page 25

29 Adjust the Angle/Energy (deg/mj) scope scales to see between -250 and 250 (see Reference [1] for help). Manually rotate the pendulum at different levels and examine the blue Pendulum Angle (deg) and the green Pendulum Energy (mj) in the Angle/Energy (deg/mj) scope. The pendulum energy is also displayed numerically in the Control Indicators section. Exercise 9: What do you notice about the energy when the pendulum is moved at different positions? Record the energy when the pendulum is being balanced (i.e. fully inverted in the upright vertical position). Click on the Stop button to bring the pendulum down to the gantry position and re-start the VI. In the Swing-Up Control Parameters section, set the Activate Swing-Up = ON (pressed) switch. If the pendulum is stationary, click on the Disturbance button in the Signal Generator section to perturb the pendulum. Exercise 10: In Swing-Up Control Parameters, change the reference energy Er between 5.0 mj and 50.0 mj. As it is varied, examine the control signal in the Voltage (V) scope as well as the blue Pendulum Angle (deg) and the red Pendulum Energy (mj) in the Angle/Energy (deg/mj) scope. Attach the response of the Angle/Energy (deg/mj) and Voltage (V) scopes. Exercise 11: In Control Parameters fix Er to 20.0 mj and vary the swing-up control gain mu between 10 and 100 m/s2/j. Describe how this changes the performance of the energy control. Click on Stop Control to disable the energy and balance controllers Hybrid Swing-Up Control Open the QNET_ROTPENT_Swing_Up_Control.vi. Ensure the correct Device is chosen. Run the QNET_ROTPENT_Swing_Up_Control.vi. In the Balance Control Parameters section verify the following parameters are set: kp_theta = V/rad kp_alpha = 80.0 V/rad kd_theta = V/(rad/s) kd_alpha = 10.5 V/(rad/s) In the Swing-Up Control Parameters section set: mu = 55 m/s2/j Er = 20.0 mj max accel = 10 m/s2 Activate Swing-Up = OFF (de-pressed) Adjust the Angle/Energy (deg/mj) scope scales to see between -250 and 250 (see Reference [1] for help). Make sure the pendulum is hanging down motionless and the encoder cable is not interfering with the pendulum. Set the Activate Swing-Up = ON (pressed) switch in the Swing-Up Control Parameters. The pendulum should begin going back and forth. If not, click on the Disturbance button in the Signal Generator section to perturb the pendulum. Turn off the Active Swing-Up switch if the pendulum goes unstable or if the encoder cable interferes with the pendulum arm Document Number 859 Revision 1.0 Page 26

30 motion. 10. Gradually increase the reference energy Er in the Control Parameters section to the energy read when the pendulum is vertically upwards (Exercise 9 in Section 4.3.4). When that reference energy is reached, the pendulum should swing-up to the inverted position. 11. Click on the Stop button to stop running the VI Exercises Exercise 1: Varying Offset Exercise 2: Arm and Pendulum Motions when Balancing Document Number 859 Revision 1.0 Page 27

31 Exercise 3: Behaviour of Arm Document Number 859 Revision 1.0 Page 28

32 Exercise 4: Response using Designed Controller Document Number 859 Revision 1.0 Page 29

33 Exercise 5: Arm Oscillation Exercise 6: Adding Dither Signal Exercise 7: Effect of Increasing Dither Frequency Document Number 859 Revision 1.0 Page 30

34 Exercise 8: Setting Dither to Measured Friction Exercise 9: Energy Level at Different Pendulum Positions Exercise 10: Changing Reference Energy Document Number 859 Revision 1.0 Page 31

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36 Exercise 11: Changing Swing-Up Gain 5. References [1] QNET User Manual [2] QNET Practical Control Guide Document Number 859 Revision 1.0 Page 33